Cognateness, frequency, and vocabulary size
An interactive account of bilingual lexical acquisition
Gonzalo Garcia-Castro1 
Daniela S. Ávila-Varela2
Ignacio Castillejo3
Núria Sebastian-Galles1
An accumulator model of word acquisition
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An accumulator model of word acquisition
For participant \(i\) and word \(j\):
\[ \begin{aligned} \text{Learning instances}_{ij} &= \text{Age}_i \cdot \text{Frequency}_j \\ \text{Frequency}_j &\sim \text{Poisson}(\lambda) \end{aligned} \]
\[ \begin{aligned} \text{Age of acquisition}_{ij} &= min(\text{Threshold}_{ij}-\text{Learning instances}_{ij}) \end{aligned} \]
We fix some parameters:
\[ \begin{aligned} \text{Threshold} &= 250 \\ \lambda &= 1 \end{aligned} \]
Simulating word acquisition
Catalan monolingual (no parallel activation)
| Catalan | Spanish |
|---|---|
| 100% | 0% |
\[ \text{Threshold} = 300 \\ \text{Frequency}_{j} \sim \text{Poisson}(\lambda) \\ \lambda = 50 \]
Simulating bilingual word acquisition
\[
\begin{aligned}
\text{Learning instances} &= Age_i \cdot Frequency_j \cdot (c \cdot Similarity_j)
\end{aligned}
\]
Simulating bilingual word acquisition
Catalan-Spanish bilingual (no parallel activation)
| Catalan | Spanish |
|---|---|
| 60% | 40% |
\[ \text{Threshold}_{ij} = 300 \\ \text{Frequency}_{j} \sim \text{Poisson}(\lambda) \\ \lambda = 50 \]
Simulating bilingual word acquisition
Catalan-Spanish bilingual (parallel activation)
| Catalan | Spanish |
|---|---|
| 75% | 25% |
\[ \text{Threshold} = 250 \\ \text{Freq. per month} \sim \text{Poisson}(1) \]
Participants
138,078 responses from 366 participants
| 1 time | 2 times | 3 times | 4 times |
|---|---|---|---|
| 312 | 42 | 8 | 4 |
Figure
Appendix
Item properties
References
Floccia, Caroline, Thomas D. Sambrook, Claire Delle Luche, Rosa Kwok, Jeremy Goslin, Laurence White, Allegra Cattani, et al. 2018. “I: Introduction.” Monographs of the Society for Research in Child Development 83 (1): 7–29. https://doi.org/10.1111/mono.12348.
Hoff, Erika, Cynthia Core, Silvia Place, Rosario Rumiche, Melissa Señor, and Marisol Parra. 2012. “Dual Language Exposure and Early Bilingual Development*.” Journal of Child Language 39 (1): 1–27. https://doi.org/10.1017/S0305000910000759.
Mitchell, Lori, Rachel K. Y. Tsui, and Krista Byers-Heinlein. 2022. “Cognates Are Advantaged in Early Bilingual Expressive Vocabulary Development.” PsyArXiv. https://doi.org/10.31234/osf.io/daktp.
